H2O + Cu(NO3)2 = HNO3 + CuO

H_2O water + Cu(NO_3)_2 copper(II) nitrate ⟶ HNO_3 nitric acid + CuO cupric oxide

Balance the chemical equation algebraically: H_2O + Cu(NO_3)_2 ⟶ HNO_3 + CuO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cu(NO_3)_2 ⟶ c_3 HNO_3 + c_4 CuO Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cu and N: H: | 2 c_1 = c_3 O: | c_1 + 6 c_2 = 3 c_3 + c_4 Cu: | c_2 = c_4 N: | 2 c_2 = c_3 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + Cu(NO_3)_2 ⟶ 2 HNO_3 + CuO

+ ⟶ +

water + copper(II) nitrate ⟶ nitric acid + cupric oxide

Construct the equilibrium constant, K, expression for: H_2O + Cu(NO_3)_2 ⟶ HNO_3 + CuO Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: H_2O + Cu(NO_3)_2 ⟶ 2 HNO_3 + CuO Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 1 | -1 Cu(NO_3)_2 | 1 | -1 HNO_3 | 2 | 2 CuO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) Cu(NO_3)_2 | 1 | -1 | ([Cu(NO3)2])^(-1) HNO_3 | 2 | 2 | ([HNO3])^2 CuO | 1 | 1 | [CuO] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2O])^(-1) ([Cu(NO3)2])^(-1) ([HNO3])^2 [CuO] = (([HNO3])^2 [CuO])/([H2O] [Cu(NO3)2])

Construct the rate of reaction expression for: H_2O + Cu(NO_3)_2 ⟶ HNO_3 + CuO Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: H_2O + Cu(NO_3)_2 ⟶ 2 HNO_3 + CuO Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 1 | -1 Cu(NO_3)_2 | 1 | -1 HNO_3 | 2 | 2 CuO | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2O | 1 | -1 | -(Δ[H2O])/(Δt) Cu(NO_3)_2 | 1 | -1 | -(Δ[Cu(NO3)2])/(Δt) HNO_3 | 2 | 2 | 1/2 (Δ[HNO3])/(Δt) CuO | 1 | 1 | (Δ[CuO])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -(Δ[H2O])/(Δt) = -(Δ[Cu(NO3)2])/(Δt) = 1/2 (Δ[HNO3])/(Δt) = (Δ[CuO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | copper(II) nitrate | nitric acid | cupric oxide formula | H_2O | Cu(NO_3)_2 | HNO_3 | CuO Hill formula | H_2O | CuN_2O_6 | HNO_3 | CuO name | water | copper(II) nitrate | nitric acid | cupric oxide

| water | copper(II) nitrate | nitric acid | cupric oxide molar mass | 18.015 g/mol | 187.55 g/mol | 63.012 g/mol | 79.545 g/mol phase | liquid (at STP) | | liquid (at STP) | solid (at STP) melting point | 0 °C | | -41.6 °C | 1326 °C boiling point | 99.9839 °C | | 83 °C | 2000 °C density | 1 g/cm^3 | | 1.5129 g/cm^3 | 6.315 g/cm^3 solubility in water | | | miscible | insoluble surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 7.6×10^-4 Pa s (at 25 °C) | odor | odorless | | |